Federer, on his secured victory, said that he is delighted to make a comeback after losing to Nishikori in his opening fixture.
Only once before has Federer failed to qualify from his group for the knockout rounds in his 15 previous appearances at the prestigious season-ending event.
Roger Federer remains in contention at the 2018 ATP Finals. Overall I thought I'm hitting the ball okay. It was disappointing but it happens.
I think we both did.
Federer, who won his 20th grand slam title at the Australian Open in January, trails only Jimmy Connors (109) in the all-time list of ATP titles.
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A quarter-final exit at Wimbledon, blowing a two-set lead against Anderson, was followed by a stunning US Open last 16 defeat to Australian journeyman John Millman.
"It needs to be said that Roger Federer is a player widely regarded as one of the biggest "box office" athletes in the world", Tiley said.
Earlier in the day, Japan's Nishikori, who beat Federer in the tournament opener, was hammered by Anderson.
Whereas he struggled for timing and was a little grumpy on Monday against Nishikori, Federer found his groove from the start against Thiem as he hunted an early break.
On account of the Japanese 2 flows through, the same number of double faults and no one implemented the break-point. Thiem visibly weakened as the set went on and, in a fitting reflection of his performance, looped an simple volley out of play to hand Federer the win.
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The 2.03-meter Anderson served 10 aces, including three in a row in the third game of the opening set.
That was all the encouragement Federer needed as he cruised to the finish line.
And the Swiss legend showed exactly that at the ATP Finals on Wednesday.
The 32-year-old Anderson, who lost just eight points on serve, was on the verge of completing just the second whitewash in the competition's history until Nishikori won the penultimate game. It was a landmark moment for Wimbledon finalist Anderson, who has set a new career-high of 47 victories in a calender year. It was a great challenge for me, I'm happy with how I played'.
"I don't really feel that I am in the mood during a World Tour Finals to discuss that topic, to be honest".
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Anderson was brimming with confidence, being nearly untouchable on serve and made some powerful returns followed by loads of pulsating groundstroke to steamroll the Japanese No. 1, serving him a nice bagel and taking the opening set 6-0. Today was a bad match.